Two spheres of masses ${\text{m}}_{\text{1}}$ and  ${\text{m}}_2$ having radius ${\text{r}}_1$ and ${\text{r}}_2$ respectively touch each other. Then the gravitational force between them is                             

Given that two spheres of masses ${\text{m}}_{\text{1}},{\text{m}}_{\text{2}}$  having radii ${\text{r}}_{\text{1}},{\text{r}}_{\text{2}}$  , centers A, B are kept in contact at C as shown

               

Now gravitational force F = ?

We can consider the entire mass of each sphere to be  concentrated at its center as point mass as shown below

Now

$\text{r}={\text{r}}_{\text{1}}+{\text{r}}_{\text{2}}$       

We know $\text{F}=\frac{\text{G}{\text{.m}}_{\text{1}}{\text{m}}_{\text{2}}}{{\text{r}}^2}$    $\Rightarrow \text{F}=\frac{\text{G}{\text{.m}}_{\text{1}}{\text{m}}_{\text{2}}}{{{\text{(r}}_{\text{1}}\text{+}{\text{r}}_{\text{2}}\text{)}}^{\text{2}}}$